Optimal learning of bandlimited functions from localized sampling

doi:10.1016/j.jco.2009.02.005

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	Optimal learning of bandlimited functions from localized sampling
	Micchelli, Charles A.2; Xu, Yuesheng 1; Zhang, Haizhang 3
	2009-04-01
发表期刊	JOURNAL OF COMPLEXITY
ISSN	0885-064X
卷号	25 期号:2 页码:85-114
摘要	An optimal algorithm for approximating bandlimited functions from localized sampling is established. Several equivalent formulations for the approximation error of the optimal algorithm are presented and its upper and lower bound estimates for the univariate case are provided. The estimates show that the approximation error decays exponentially (but not faster) as the number of localized samplings increases. As a consequence of these results, we obtain an upper bound estimate for the eigenvalues of an integral operator that arises in the bandwidth problem. (C) 2009 Elsevier Inc. All rights reserved.
关键词	Whittaker-Shannon series Bandlimited signals Optimal algorithms Error estimates Translation invariant kernels The bandwidth problem
DOI	10.1016/j.jco.2009.02.005
语种	英语
资助项目	US National Science Foundation[DMS-0712827] ; US National Science Foundation[CCR-0407476] ; Natural Science Foundation of China[10371122] ; Natural Science Foundation of China[10631080] ; Education Ministry of the People's Republic of China through Sun Yat-sen University
WOS研究方向	Computer Science ; Mathematics
WOS类目	Computer Science, Theory & Methods ; Mathematics, Applied
WOS记录号	WOS:000265303600001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7637
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Yuesheng
作者单位	1.Syracuse Univ, Dept Math, Syracuse, NY 13244 USA 2.SUNY Albany, Dept Math & Stat, Albany, NY 12222 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Micchelli, Charles A.,Xu, Yuesheng,Zhang, Haizhang. Optimal learning of bandlimited functions from localized sampling[J]. JOURNAL OF COMPLEXITY,2009,25(2):85-114.
APA	Micchelli, Charles A.,Xu, Yuesheng,&Zhang, Haizhang.(2009).Optimal learning of bandlimited functions from localized sampling.JOURNAL OF COMPLEXITY,25(2),85-114.
MLA	Micchelli, Charles A.,et al."Optimal learning of bandlimited functions from localized sampling".JOURNAL OF COMPLEXITY 25.2(2009):85-114.